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High-temperature materials and creep

The steady-state creep rate of a heat-resistant alloy follows the power law ε̇ = Aσⁿexp(−Q/RT) with a stress exponent of n = 5. If the stress is raised by 20% at the same temperature, by roughly what factor does the steady-state creep rate increase?

  1. AAbout 2.5 times
  2. BAbout 6.0 times
  3. CAbout 1.2 times
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Answer: A. About 2.5 times

At the same temperature A and exp(−Q/RT) do not change, so the ratio of the rates is the stress ratio raised to the power n: (1.2)⁵ ≈ 2.49, about 2.5 times. That a mere 20% increase in stress more than doubles the rate is characteristic of dislocation creep (power-law creep), where n is large, about 3 to 8, and a small error in the design stress greatly affects the life. About 6.0 times is the value obtained by multiplying the stress ratio by the exponent n, and about 1.2 times assumes that the rate is proportional to stress (n = 1), which is the case for diffusion creep operating at low stress. Plotting rate against stress on log-log axes gives a slope of n.

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More High-temperature materials and creep questions

  1. An alloy has a steady-state creep rate that follows ε̇ = Aσⁿexp(−Q/RT) with an activation energy of Q = 300 kJ/mol. If the temperature is raised from 1000 K to 1050 K at the same stress, by roughly what factor does the steady-state creep rate increase? Take R = 8.314 J/(mol·K).
  2. A fine-grained polycrystalline metal was creep tested at a low stress at about 0.5 times its melting point (in absolute temperature). The steady-state creep rate was nearly proportional to stress (stress exponent n ≈ 1) and nearly inversely proportional to the cube of the grain size. Which creep mechanism is most likely to be operating?
  3. Which statement about the deformation mechanism map of Ashby and coworkers (with stress normalized by the shear modulus, σ/G, on the vertical axis and homologous temperature T/Tm on the horizontal axis) is correct? Tm is the melting point in absolute temperature.
  4. At room temperature, refining the grains raises strength (the Hall–Petch relation), but components loaded for long times at high temperature often use coarse grains or single crystals. Which is the correct reason?
  5. A heat-resistant alloy ruptured by creep in 1000 h at 1000 K under a certain stress. Assuming the Larson–Miller parameter P = T(C + log₁₀t_r) (T is the absolute temperature, t_r is the rupture time in h, and C = 20) is constant at the same stress, which temperature is closest to that giving a rupture life of 10⁵ h at the same stress?